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Bosnia and Herzegovina TST 1998 Day 2 Problem 1

Source: Bosnia and Herzegovina Team Selection Test 1998

September 20, 2018

circletangentgeometryperpendicular

Problem Statement

Circle

k

with radius

r

touches the line

p

in point

E

. Let

CD

be a dimeter of circle and

D

an arbitrary point of circle distinct from points

ED=BC

and

B

. Let

D

be a foot of perpendicular from point

C

to line

AB

. Let

E

be a point on extension of line

CD

, over point

D

, such that

ED=BC

. Let tangents on circle from point

E

intersect line

p

in points

K

and

N

. Prove that length of

KN

does not depend from

C

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